Articles and Tutorials — video

Dancing Pyramids Origami Tessellation

Posted by Madonna Yoder on

Dancing Pyramids Origami Tessellation

A Whole Lot of 3   Sometimes it can be hard to tell what's 3 and what's 6. Now this may sound confusing - how can you not know the difference between 3 and 6? But when there's 6 things, with alternation between each one, is it 3 or is it 6? In terms of rotational symmetry, the answer is 3. In terms of twists in a loop, the answer is 6. And to make matters worse, you can't look for 3-fold symmetries around the point in question to decide - they're all going to be 3-fold in either case!...

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How to Fold Your First Tessellation

Posted by Madonna Yoder on

How to Fold Your First Tessellation

Managing many pleats at once is one of the harder things about tessellations, but using these three-way intersections one at a time lets us minimize the difficulty and focus on the steps.

These three-way intersections can be put together in a huge variety of ways, from rotational to mirrored to combinations of both.

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How to Start with Tessellations

Posted by Madonna Yoder on

How to Start with Tessellations

Many folders would like to start learning tessellations, but aren't sure where to start. In this video I introduced the four major grid types that every tessellation folder needs to know and clarified the distinction between twist-based tessellations, corrugations, and tessellations that require an all-at-once collapse. You see, there are easier and harder ways to fold tessellations and when many folders see a crease pattern for the first time they think that they need to precrease everything and then collapse all at once. That's actually the hardest way to learn tessellations - you have more work at the beginning, more...

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Purl Origami Tessellation

Posted by Madonna Yoder on

Purl Origami Tessellation

Patterns in the Tessellation   You can see many things in any tessellation - here I'm seeing a close mimic of the purl knitting stitch, and also an Easter bunny. I'm also seeing parallel mirror symmetry lines with a string of twists between them, a sequence of triangle-rhombus-triangle that I use in many tessellations, and an unusual arrangement of rhombi and triangles. Which aspect I choose to emphasize varies with the lighting, the level of zoom, and who I'm talking to.   Details As we look closely at this tessellation, we can see that there's the zigzagging rhombi and triangles,...

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Hybrid Closed Islands Origami Tessellation

Posted by Madonna Yoder on

Hybrid Closed Islands Origami Tessellation

Tiling Surprise Believe it or not, Hybrid Closed Islands has the same tiling structure as Robin Scholz's Celtic Circle. Both of these tessellations feature twists with six pleats (hexagon twists) surrounded by twists with three pleats (triangle twists) and vice versa. However, when you look at Hybrid Closed Islands it's easy to see only triangles - because the six-pleated twists only have three-fold rotational symmetry.   Centering Choices In this tessellation, I have three equivalent choices of what to put in the center, and whatever I put in the center will be emphasized in the pattern. Each of these three...

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